Question: Solve for $x$ and $y$ using elimination. ${-3x-4y = -44}$ ${3x+3y = 36}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $-y = -8$ $\dfrac{-y}{{-1}} = \dfrac{-8}{{-1}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-3x-4y = -44}\thinspace$ to find $x$ ${-3x - 4}{(8)}{= -44}$ $-3x-32 = -44$ $-3x-32{+32} = -44{+32}$ $-3x = -12$ $\dfrac{-3x}{{-3}} = \dfrac{-12}{{-3}}$ ${x = 4}$ You can also plug ${y = 8}$ into $\thinspace {3x+3y = 36}\thinspace$ and get the same answer for $x$ : ${3x + 3}{(8)}{= 36}$ ${x = 4}$